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\@writefile{toc}{\contentsline {section}{\numberline {3}设函数 $f(x)$ 在区间 $[a,+\infty )$ 上连续,在 $(a,+\infty )$ 上可 导, 且 $f^{\prime }(x)$ 严格单调递增,求证：$F(h)=\genfrac  {}{}{}0{f(a+h)-f(a)}{h}$ 关于 $h$ 也严格单调递增.}{3}\protected@file@percent }
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\@writefile{toc}{\contentsline {section}{\numberline {12}求椭圆 $\genfrac  {}{}{}0{x^{2}}{a^{2}}+\genfrac  {}{}{}0{y^{2}}{b^{2}}=1$ 在第一象限中的切线,使得它和坐标轴所围三角形面积最小.}{8}\protected@file@percent }
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\@writefile{toc}{\contentsline {section}{\numberline {15}设 $f(x)$ 是区间 $(a, b)$ 上的凸函数. 证明 : 对任意的 $x \in (a, b), f(x)$ 在 $x$ 点处连续, 且存在左右导数.(注意:凸函数的定义中并没有预先假设函数连续. )}{11}\protected@file@percent }
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